NONTECHNICAL SUMMARY<br/><br/>This award supports theoretical research with a general aim to understand, predict, and control novel regimes of matter in light-driven quantum materials. Our understanding of light-matter interaction has been instrumental in technological applications such as solar cells, phototransistors, and light-emitting diodes. However, recent advances in probes accessing and manipulating quantum states in time and length scales that were unattainable just a decade ago have now enabled the exploration of new quantum phases of matter, leading to many questions and challenges. Questions on light-driven engineering of materials, such as "How fast and drastically can we change the properties of materials using light?" or "Can light induce states in matter that can revolutionize quantum computation?" demand a concerted theoretical effort to understand the dynamics of photon-dressed electrons and the phases of light-driven matter. This project aims to establish the theoretical foundations of physical phenomena in periodically driven systems where light irradiation offers precise control of material properties and can induce novel non-equilibrium states of technological relevance.<br/><br/>This award will also support the training of undergraduate students through direct involvement in the PI’s research, aid the creation of educational materials and resources that will train high-school teachers, and expose high-school students to the concepts of materials physics and light-matter interactions. This project will, in addition, help the establishment of collaborations with national and international researchers and increase the retention and enrollment of students from historically underserved communities in physics.<br/><br/>TECHNICAL SUMMARY<br/><br/>This award supports theoretical research to develop techniques, methodologies, and model systems for understanding periodically-driven systems and predicting and controlling novel regimes of matter in existing and future experimental setups. Systems that intertwine light-matter, magnetic, and spin-orbit interactions will be the primary focus of the research that will be carried out in two major thrusts. In the first thrust, the PI will investigate light-driven effects on spin-susceptibility and the indirect magnetic exchange interaction mediated by irradiated materials with spin-orbit-coupling (SOC). The PI will calculate the induced magnetic exchange interaction between magnetic adatoms in light-driven two-dimensional SOC materials and irradiated magnetic heterostructures enclosing three-dimensional Rashba coupled semiconductors. The theory developed will quantify the magnetic exchange coupling mediated by photon-dressed fermions in irradiated SOC systems. The second thrust is focused on light-matter interactions in Dirac-like materials subjected to light-vortex beams. The PI will develop a theory to describe these time and space-dependent systems, explore new phenomena arising from light’s orbital angular momentum, and analyze the potential photoinduction of vortices and concomitant vortex states to establish ways to observe these predictions in experiments.<br/><br/>This award will also support the creation of educational materials and resources to be used by high-school teachers and undergraduates, and expose high-school students to the concepts of condensed matter physics and light-matter interactions through the PI’s research. This project will help increase the retention and enrollment of students from historically underserved communities in physics and will aid the establishment of collaborations with national and international researchers.<br/><br/>This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.